Vector Algebra

Two adjacent sides of a parallelogram $A B C D$ are given by $\overline{\mathrm{AB}}=2 \hat{\mathrm{i}}+10 \hat{\mathrm{j}}+11 \hat{\mathrm{k}}$ and $\overline{\mathrm{AD}}=-\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}$. The side AD is rotated by an acute angle $\alpha$ in the plane of parallelogram so that AD becomes $\mathrm{AD}^{\prime}$. If $\mathrm{AD}^{\prime}$ makes a right angle with the side AB , then $\cos \alpha=$